Glad that I wasn't bringing bad news there!
If he breeds a Leghorn hen, and they are both well bred birds, then yes, you should get more white Leghorns.
I would expect at least a few years out of them, and even then they will still lay, just less regularly; I have an eight year old hen that still lays about two eggs a week. With the Leghorns and the BSLs, you may start to see reproductive issues after 4-5 years. If you're looking to sustainably produce eggs, I would add new birds (and as you have your cockerel, you can hatch your own) every 2-3 years to ensure a good supply.
I run a mixed flock in this manner, hatching out every year and retaining pullets for production whilst still keeping my older hens. I never keep a cockerel hatched from my own eggs, but rather buy in hatching eggs (I run a closed flock) and keep a cockerel from those whenever I need one; in this way I am able to maintain a good amount of genetic diversity to avoid inbreeding.